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A361020 Lexicographically earliest infinite sequence such that a(i) = a(j) => A343029(i) = A343029(j) and A343030(i) = A343030(j) for all i, j >= 0.

%I A361020 #13 Mar 04 2023 17:07:41
%S A361020 1,2,3,4,2,5,6,7,3,4,5,8,4,9,10,11,2,5,6,7,5,8,9,12,6,7,8,13,7,14,15,
%T A361020 16,3,4,5,8,4,9,10,11,5,8,9,12,8,13,14,17,4,9,10,11,9,12,13,18,10,11,
%U A361020 12,19,11,20,21,22,2,5,6,7,5,8,9,12,6,7,8,13,7,14,15,16,5,8,9,12,8,13,14,17,9,12,13,18,12,19,20,23,6,7,8
%N A361020 Lexicographically earliest infinite sequence such that a(i) = a(j) => A343029(i) = A343029(j) and A343030(i) = A343030(j) for all i, j >= 0.
%C A361020 Restricted growth sequence transform of the ordered pair [A343029(n), A343030(n)].
%C A361020 For all i, j >= 0:
%C A361020   a(i) = a(j) => A000120(i) = A000120(j),
%C A361020   a(i) = a(j) => A004718(i) = A004718(j) => A361016(i) = A361016(j).
%C A361020 Because the Danish composer Per Nørgård's "infinity sequence" (A004718) can be represented as an difference A343029(n) - A343030(n), it is a function of this sequence, whose scatter plot shows interesting structure. (The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.)
%H A361020 Antti Karttunen, <a href="/A361020/b361020.txt">Table of n, a(n) for n = 0..65537</a>
%H A361020 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A361020 (PARI)
%o A361020 up_to = 65537;
%o A361020 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A361020 A343029(n) = { my(t=1, ret=0); for(i=0, if(n, logint(n, 2)), if(bittest(n, i), ret+=t, t=!t)); ret; }; \\ From A343029
%o A361020 A343030(n) = { my(t=0, ret=0); for(i=0, if(n, logint(n, 2)), if(bittest(n, i), ret+=t, t=!t)); ret; }; \\ From A343030
%o A361020 Aux361020(n) = [A343029(n), A343030(n)];
%o A361020 v361020 = rgs_transform(vector(1+up_to,n,Aux361020(n-1)));
%o A361020 A361020(n) = v361020[1+n];
%Y A361020 Cf. A343029, A343030.
%Y A361020 Cf. A000120, A004718, A361016.
%Y A361020 Cf. also A286622.
%K A361020 nonn,look
%O A361020 0,2
%A A361020 _Antti Karttunen_, Mar 03 2023